A concave mirror has a radius of curvature of 0.975 m. An object is placed 2.08 m in front of the mirror.
What is the position of the image?
The focal point is half the radius of curvature.
1/do+1/di=1/f=2/radius
To determine the position of the image formed by a concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the distance of the image from the mirror
- u is the distance of the object from the mirror
First, let's calculate the focal length of the concave mirror using the formula:
f = R/2
Where:
- R is the radius of curvature of the mirror
Given that the radius of curvature (R) is 0.975 m, we can calculate the focal length (f):
f = 0.975 m / 2 = 0.4875 m
Now, let's substitute the values of f and u into the mirror formula to find v:
1/0.4875 = 1/v - 1/2.08
Rearranging the equation:
1/v = 1/0.4875 + 1/2.08
Calculating the values:
1/v = 2.05 + 0.4817
1/v = 2.5317
Now, invert both sides of the equation to get v:
v = 1 / (1/v) = 1 / 2.5317
v ≈ 0.395 m
Therefore, the position of the image formed by the concave mirror is approximately 0.395 meters from the mirror.